The CT Company produces two products$-A^{}$ and $B.$ According to the past

experience, production of either product $A$ or product $B$ requires an average of one hour in

the plant. The plant has a normal production capacity of $300$ hours a month. The marketing

department of the firm reports that because of limited market, the maximum number of

product A and product $B$ that can be sold in a month are $140$ and $200$ respectively. The net

profit from the sale of product A and product B are Rs$.600$ and Rs$.200$ respectively. The

manager has set the following goals.

$P_1$ : The first goal is to avoid any underutilization of normal production capacity.

$P_2$ : He wants to sell maximum possible units of product A and $B.$ Since the net profit from

the sale of product $A$ is thrice the amount from Product $B,$ therefore, the manager has

thrice as much desire to achieve sales for product $A$ as for Product $B.$

$P_3.$ He wants to minimize the overtime operation of the plant as much as possible.

Formulate the Goal programming problem.